In the past few decades, the petroleum industry has invested heavily in the development of marine seismic survey techniques that yield knowledge of subterranean formations beneath a body of water in order to find and extract valuable mineral resources, such as oil. High-resolution seismic images of a subterranean formation are essential for quantitative seismic interpretation and improved reservoir monitoring. For a typical marine seismic survey, an exploration-seismology vessel tows a seismic source and one or more streamers that form a seismic data acquisition surface below the surface of the water and over a subterranean formation to be surveyed for mineral deposits. The vessel contains seismic acquisition equipment, such as navigation control, seismic source control, seismic receiver control, and recording equipment. The seismic source control causes the seismic source, which is typically an array of source elements, such as air guns, to produce acoustic impulses at selected times. Each impulse is a sound wave that travels down through the water and into the subterranean formation. At each interface between different types of rock, a portion of the sound wave is refracted, a portion of the sound wave is transmitted, and another portion is reflected back toward the body of water to propagate toward the surface. The streamers towed behind the vessel are elongated cable-like structures. Each streamer includes a number of seismic receivers or sensors that detect pressure and/or velocity wavefields associated with the sound waves reflected back into the water from the subterranean formation.
In order to process seismic data measured at the acquisition surface to produce focused seismic images of a subterranean formation, accurate knowledge of a pressure wavefield created by the seismic source is desired. However, obtaining an accurate characterization of the source pressure wavefield is often met with difficulty. For example, the source pressure wavefield can be determined from pressure measurements taken within near fields of the source elements, but the measurements can be contaminated with noise caused by cross-talk and from the hydrophones picking up some of the motion caused by firing other powerful source elements in the vicinity of the hydrophone. Other techniques to accurately characterize the source pressure wavefield include modeling the source pressure wavefield. The models are typically calibrated with actual measurements taken at far-field distances from the source elements and rely on a number of input parameters, such as positions of the source elements, pressures, and water temperature. Predominant errors in source wavefield modeling are typically related to the accuracy of the calibration and the assumptions made in modeling. As a result, those working in the petroleum industry continue to seek systems and methods to more accurately characterize the source pressure wavefield.